Bellman function approach to the sharp constants in uniform convexity

We illustrate Bellman function technique in finding the modulus of uniform convexity of $L^{p}$ spaces.Comment: 5 page

A bundling problem revisited

It was conjectured by M. Glasser and S. Davison and later proved by A. Eremenko that the certain animals should gather close to each other in order to decrease the total heat loss. In this paper we show that it is not always true for the individual heat loss. This gives a negative answer to a question posed by A. Eremenko